"""
LES Turbulence Demo - Turbulent Channel Flow

This example demonstrates Large Eddy Simulation (LES) for turbulent channel flow
using various subgrid-scale models. It showcases the turbulence modeling
capabilities of NSEMSolver.jl for high Reynolds number flows.

Key Physics Demonstrated:
- Large Eddy Simulation (LES) with spectral element methods
- Subgrid-scale modeling (Smagorinsky, Dynamic Smagorinsky, WALE)
- Explicit filtering operations for LES
- Turbulent statistics computation
- Wall-bounded turbulent flows
- Turbulent kinetic energy cascades

Problem Setup:
- Turbulent channel flow between parallel plates
- Reynolds numbers from Re_τ = 180 to 1000 (friction Reynolds number)
- Periodic boundary conditions in streamwise direction
- No-slip walls at top and bottom
- Various subgrid-scale closure models
"""

using NSEMSolver
using Printf
using Statistics

"""
    run_les_turbulence_demo(; Re_tau=395, turbulence_model=:smagorinsky, 
                           resolution=64, verbose=true)

Run LES turbulent channel flow simulation.

# Arguments
- `Re_tau::Float64`: Friction Reynolds number Re_τ = u_τ*h/ν (default: 395)
- `turbulence_model::Symbol`: Subgrid model (:smagorinsky, :dynamic, :wale)
- `resolution::Int`: Grid resolution parameter (default: 64)
- `verbose::Bool`: Enable detailed output (default: true)

# Returns
- `LESResult`: Complete LES simulation results with turbulence statistics
"""
function run_les_turbulence_demo(; Re_tau::Float64=395, turbulence_model::Symbol=:smagorinsky, 
                                 resolution::Int=64, verbose::Bool=true)
    
    if verbose
        println("🌪️ LES Turbulence Demo - Turbulent Channel Flow")
        println("===============================================")
        println("Friction Reynolds number: Re_τ = $(Re_tau)")
        println("Subgrid-scale model: $(turbulence_model)")
        println("Grid resolution: $(resolution)")
        println()
    end
    
    # Channel geometry
    h = 1.0              # Half-channel height (m)
    L_x = 4π * h         # Streamwise length (typical for channel flow)
    L_y = 2 * h          # Channel height
    L_z = 2π * h         # Spanwise length (for 3D, here we do 2D)
    
    # Flow properties based on friction Reynolds number
    # Re_τ = u_τ*h/ν, where u_τ is friction velocity
    
    # For air at standard conditions
    ν = 1.5e-5           # Kinematic viscosity (m²/s)
    u_tau = Re_tau * ν / h    # Friction velocity
    
    # Bulk velocity (approximate relationship for channel flow)
    Re_b = Re_tau * 18.7  # Approximate conversion Re_bulk ≈ 18.7 * Re_τ
    U_b = Re_b * ν / h    # Bulk velocity
    
    if verbose
        println("Computed flow parameters:")
        println("  Channel half-height: h = $(h) m")
        println("  Streamwise length: L_x = $(L_x) m")
        println("  Friction velocity: u_τ = $(u_tau) m/s")
        println("  Bulk velocity: U_b ≈ $(U_b) m/s")
        println("  Kinematic viscosity: ν = $(ν) m²/s")
        println("  Bulk Reynolds number: Re_b ≈ $(Re_b)")
        println()
    end
    
    # Base Navier-Stokes solver options
    ns_options = NSOptions(
        N = 4,                              # Polynomial order
        nu = ν,                             # Kinematic viscosity
        cfl = 0.3,                          # Conservative CFL for LES
        tfinal = 20.0,                      # Final time (multiple flow-through times)
        dim = 2,                            # 2D LES (simplified)
        n_block = div(resolution, 4),       # Number of spectral elements
        max_steps = 8000,                   # Maximum time steps
        tol = 1e-7,                        # Convergence tolerance
        solver = :julia,                    # Linear solver
        verbose = verbose
    )
    
    # Create turbulence model
    sgs_model = create_turbulence_model(turbulence_model, h, Re_tau)
    
    if verbose
        println("Turbulence model details:")
        println("  Type: $(typeof(sgs_model))")
        if sgs_model isa SmagorinskyModel
            println("  Smagorinsky constant: C_s = $(sgs_model.C_s)")
            println("  Filter width: Δ = $(sgs_model.filter_width)")
        elseif sgs_model isa DynamicSmagorinskyModel
            println("  Test filter ratio: $(sgs_model.test_filter_ratio)")
            println("  Coefficient clipping: $(sgs_model.clip_coefficient)")
        elseif sgs_model isa WALEModel
            println("  WALE constant: C_w = $(sgs_model.C_w)")
        end
        println()
    end
    
    if verbose
        println("Expected turbulence characteristics:")
        println("  Friction time scale: t_τ = h/u_τ = $(h/u_tau) s")
        println("  Viscous length scale: l_ν = ν/u_τ = $(ν/u_tau) m")
        println("  Kolmogorov length scale: η ≈ $(estimate_kolmogorov_scale(Re_tau, h)) m")
        println("  Taylor microscale: λ ≈ $(estimate_taylor_scale(Re_tau, h)) m")
        println()
        println("Starting LES simulation...")
    end
    
    # Run LES simulation
    result = solve_les_flow_2d(ns_options, sgs_model)
    
    if verbose
        print_les_turbulence_results(result, Re_tau, h, u_tau)
    end
    
    return result
end

"""
    create_turbulence_model(model_type, h, Re_tau) -> TurbulenceModel

Create turbulence model with appropriate parameters for channel flow.
"""
function create_turbulence_model(model_type::Symbol, h::Float64, Re_tau::Float64)
    # Filter width (grid scale)
    Δ = h / 20  # Typical LES filter width
    
    if model_type == :smagorinsky
        return SmagorinskyModel(
            C_s = 0.17,                    # Standard Smagorinsky constant
            filter_width = Δ,
            van_driest_damping = true,     # Enable wall damping
            wall_distance_required = false
        )
        
    elseif model_type == :dynamic
        return DynamicSmagorinskyModel(
            test_filter_ratio = 2.0,       # Standard test filter ratio
            clip_coefficient = true,       # Prevent negative viscosity
            averaging_direction = :local,   # Local averaging
            minimum_coefficient = 0.0
        )
        
    elseif model_type == :wale
        return WALEModel(
            C_w = 0.325,                   # Standard WALE constant
            filter_width = Δ
        )
        
    else
        throw(ArgumentError("Unknown turbulence model: $(model_type)"))
    end
end

"""
    estimate_kolmogorov_scale(Re_tau, h) -> Float64

Estimate Kolmogorov microscale for channel flow.
"""
function estimate_kolmogorov_scale(Re_tau::Float64, h::Float64)
    # η/h ≈ Re_τ^(-3/4) for channel flow
    return h * Re_tau^(-0.75)
end

"""
    estimate_taylor_scale(Re_tau, h) -> Float64

Estimate Taylor microscale for channel flow.
"""
function estimate_taylor_scale(Re_tau::Float64, h::Float64)
    # λ/h ≈ Re_τ^(-1/2) for channel flow
    return h * Re_tau^(-0.5)
end

"""
    print_les_turbulence_results(result, Re_tau, h, u_tau)

Print comprehensive LES turbulence results.
"""
function print_les_turbulence_results(result::LESResult, Re_tau::Float64, h::Float64, u_tau::Float64)
    println("\\n" * "="^70)
    println("LES TURBULENCE SIMULATION RESULTS")
    println("="^70)
    
    # Simulation diagnostics
    println("Simulation Status:")
    println("  Converged: $(result.converged)")
    println("  Time steps: $(result.iterations)")
    println("  Solve time: $(result.solve_time) seconds")
    println("  Final residual: $(result.residual_norm)")
    println()
    
    # Turbulence model info
    println("Turbulence Model:")
    println("  Type: $(typeof(result.turbulence_model))")
    println("  Target Re_τ: $(Re_tau)")
    println()
    
    # Flow field statistics
    if !isnothing(result.u) && !isnothing(result.v)
        u_stats = compute_velocity_statistics(result.u, result.v, h, u_tau)
        print_velocity_statistics(u_stats)
    end
    
    # Subgrid-scale statistics
    if !isnothing(result.nu_sgs)
        sgs_stats = compute_sgs_statistics(result.nu_sgs, result.options.nu)
        print_sgs_statistics(sgs_stats)
    end
    
    # Turbulence statistics from result
    turb_stats = result.turbulence_statistics
    println("Turbulence Statistics:")
    for (key, value) in turb_stats
        println("  $(key): $(value)")
    end
    println()
    
    # Energy cascade analysis
    if !isnothing(result.strain_rate) && !isnothing(result.nu_sgs)
        cascade_stats = analyze_energy_cascade(result.strain_rate, result.nu_sgs, result.options.nu)
        print_cascade_analysis(cascade_stats)
    end
    
    println("="^70)
end

"""
    compute_velocity_statistics(u, v, h, u_tau) -> Dict

Compute detailed velocity statistics for channel flow.
"""
function compute_velocity_statistics(u::Array{Float64,2}, v::Array{Float64,2}, h::Float64, u_tau::Float64)
    stats = Dict{String,Any}()
    
    # Basic statistics
    stats["u_mean"] = mean(u)
    stats["v_mean"] = mean(v)
    stats["u_rms"] = sqrt(mean(u.^2))
    stats["v_rms"] = sqrt(mean(v.^2))
    stats["u_max"] = maximum(abs.(u))
    stats["v_max"] = maximum(abs.(v))
    
    # Velocity magnitude statistics
    velocity_mag = sqrt.(u.^2 + v.^2)
    stats["velocity_magnitude_mean"] = mean(velocity_mag)
    stats["velocity_magnitude_max"] = maximum(velocity_mag)
    
    # Reynolds stress approximation (from fluctuations)
    u_fluct = u .- mean(u)
    v_fluct = v .- mean(v)
    stats["reynolds_stress_uv"] = mean(u_fluct .* v_fluct)
    
    # Turbulence intensity
    stats["turbulence_intensity_u"] = sqrt(mean(u_fluct.^2)) / abs(mean(u))
    stats["turbulence_intensity_v"] = sqrt(mean(v_fluct.^2)) / abs(mean(u))
    
    # Wall-normalized quantities
    stats["u_plus_max"] = maximum(abs.(u)) / u_tau
    stats["u_rms_plus"] = sqrt(mean(u.^2)) / u_tau
    
    return stats
end

"""
    print_velocity_statistics(stats)

Print velocity statistics in organized format.
"""
function print_velocity_statistics(stats::Dict{String,Any})
    println("Velocity Field Statistics:")
    println("  Mean u velocity: $(get(stats, \"u_mean\", \"N/A\")) m/s")
    println("  Mean v velocity: $(get(stats, \"v_mean\", \"N/A\")) m/s")
    println("  RMS u velocity: $(get(stats, \"u_rms\", \"N/A\")) m/s")
    println("  RMS v velocity: $(get(stats, \"v_rms\", \"N/A\")) m/s")
    println("  Max |u| velocity: $(get(stats, \"u_max\", \"N/A\")) m/s")
    println("  Max |v| velocity: $(get(stats, \"v_max\", \"N/A\")) m/s")
    println("  Mean velocity magnitude: $(get(stats, \"velocity_magnitude_mean\", \"N/A\")) m/s")
    println("  Max velocity magnitude: $(get(stats, \"velocity_magnitude_max\", \"N/A\")) m/s")
    println()
    
    println("Turbulence Characteristics:")
    println("  Reynolds stress ⟨u'v'⟩: $(get(stats, \"reynolds_stress_uv\", \"N/A\")) m²/s²")
    println("  Turbulence intensity (u): $(get(stats, \"turbulence_intensity_u\", \"N/A\") * 100)%")
    println("  Turbulence intensity (v): $(get(stats, \"turbulence_intensity_v\", \"N/A\") * 100)%")
    println()
    
    println("Wall-Normalized Quantities:")
    println("  u⁺_max: $(get(stats, \"u_plus_max\", \"N/A\"))")
    println("  u⁺_rms: $(get(stats, \"u_rms_plus\", \"N/A\"))")
    println()
end

"""
    compute_sgs_statistics(nu_sgs, nu_molecular) -> Dict

Compute subgrid-scale viscosity statistics.
"""
function compute_sgs_statistics(nu_sgs::Array{Float64,2}, nu_molecular::Float64)
    stats = Dict{String,Any}()
    
    stats["nu_sgs_mean"] = mean(nu_sgs)
    stats["nu_sgs_max"] = maximum(nu_sgs)
    stats["nu_sgs_std"] = std(nu_sgs)
    stats["viscosity_ratio_mean"] = mean(nu_sgs) / nu_molecular
    stats["viscosity_ratio_max"] = maximum(nu_sgs) / nu_molecular
    
    # Percentage of domain with significant SGS viscosity
    significant_threshold = 0.1 * nu_molecular
    stats["sgs_active_percentage"] = 100 * sum(nu_sgs .> significant_threshold) / length(nu_sgs)
    
    return stats
end

"""
    print_sgs_statistics(stats)

Print subgrid-scale viscosity statistics.
"""
function print_sgs_statistics(stats::Dict{String,Any})
    println("Subgrid-Scale Viscosity Statistics:")
    println("  Mean νₛₘ: $(get(stats, \"nu_sgs_mean\", \"N/A\")) m²/s")
    println("  Max νₛₘ: $(get(stats, \"nu_sgs_max\", \"N/A\")) m²/s")
    println("  Std Dev νₛₘ: $(get(stats, \"nu_sgs_std\", \"N/A\")) m²/s")
    println("  Mean viscosity ratio ⟨νₛₘ/ν⟩: $(get(stats, \"viscosity_ratio_mean\", \"N/A\"))")
    println("  Max viscosity ratio (νₛₘ/ν)_max: $(get(stats, \"viscosity_ratio_max\", \"N/A\"))")
    println("  Percentage with active SGS: $(get(stats, \"sgs_active_percentage\", \"N/A\"))%")
    println()
end

"""
    analyze_energy_cascade(strain_rate, nu_sgs, nu) -> Dict

Analyze energy cascade characteristics.
"""
function analyze_energy_cascade(strain_rate::Array{Float64,2}, nu_sgs::Array{Float64,2}, nu::Float64)
    stats = Dict{String,Any}()
    
    # Strain rate statistics
    stats["strain_rate_mean"] = mean(strain_rate)
    stats["strain_rate_max"] = maximum(strain_rate)
    
    # Energy dissipation rates
    molecular_dissipation = 2 * nu * mean(strain_rate.^2)
    sgs_dissipation = 2 * mean(nu_sgs .* strain_rate.^2)
    total_dissipation = molecular_dissipation + sgs_dissipation
    
    stats["molecular_dissipation"] = molecular_dissipation
    stats["sgs_dissipation"] = sgs_dissipation
    stats["total_dissipation"] = total_dissipation
    stats["sgs_dissipation_fraction"] = sgs_dissipation / total_dissipation
    
    return stats
end

"""
    print_cascade_analysis(stats)

Print energy cascade analysis results.
"""
function print_cascade_analysis(stats::Dict{String,Any})
    println("Energy Cascade Analysis:")
    println("  Mean strain rate: $(get(stats, \"strain_rate_mean\", \"N/A\")) 1/s")
    println("  Max strain rate: $(get(stats, \"strain_rate_max\", \"N/A\")) 1/s")
    println("  Molecular dissipation: $(get(stats, \"molecular_dissipation\", \"N/A\")) m²/s³")
    println("  SGS dissipation: $(get(stats, \"sgs_dissipation\", \"N/A\")) m²/s³")
    println("  Total dissipation: $(get(stats, \"total_dissipation\", \"N/A\")) m²/s³")
    println("  SGS dissipation fraction: $(get(stats, \"sgs_dissipation_fraction\", \"N/A\") * 100)%")
    println()
end

"""
    run_sgs_model_comparison(; Re_tau=395, resolution=48)

Compare different subgrid-scale models for the same flow conditions.
"""
function run_sgs_model_comparison(; Re_tau::Float64=395, resolution::Int=48)
    println("🔬 LES Subgrid-Scale Model Comparison")
    println("====================================")
    println("Friction Reynolds number: Re_τ = $(Re_tau)")
    println("Grid resolution: $(resolution)")
    println()
    
    models = [:smagorinsky, :dynamic, :wale]
    results = Dict{Symbol,Any}()
    
    for (i, model) in enumerate(models)
        println("Model $(i)/$(length(models)): $(model)")
        println("-" * "="^40)
        
        result = run_les_turbulence_demo(Re_tau=Re_tau, turbulence_model=model, 
                                        resolution=resolution, verbose=false)
        results[model] = result
        
        # Print key statistics
        turb_stats = result.turbulence_statistics
        max_nu_sgs = get(turb_stats, "max_subgrid_viscosity", NaN)
        mean_nu_sgs = get(turb_stats, "mean_subgrid_viscosity", NaN)
        tke = get(turb_stats, "turbulent_kinetic_energy_estimate", NaN)
        
        println("  Max νₛₘ: $(max_nu_sgs) m²/s")
        println("  Mean νₛₘ: $(mean_nu_sgs) m²/s")
        println("  TKE estimate: $(tke) m²/s²")
        println("  Converged: $(result.converged)")
        println()
    end
    
    # Comparison summary
    println("SGS MODEL COMPARISON SUMMARY")
    println("="^60)
    println("Model\\t\\t\\tMax νₛₘ\\t\\tMean νₛₘ\\t\\tTKE")
    println("-"^60)
    
    for model in models
        result = results[model]
        stats = result.turbulence_statistics
        max_nu_sgs = get(stats, "max_subgrid_viscosity", NaN)
        mean_nu_sgs = get(stats, "mean_subgrid_viscosity", NaN)  
        tke = get(stats, "turbulent_kinetic_energy_estimate", NaN)
        
        @printf "%-15s\\t%.2e\\t%.2e\\t%.2e\\n" string(model) max_nu_sgs mean_nu_sgs tke
    end
    
    return results
end

"""
    run_reynolds_scaling_study(; Re_tau_range=[180, 395, 590], model=:smagorinsky)

Study Reynolds number scaling effects on LES results.
"""
function run_reynolds_scaling_study(; Re_tau_range::Vector{Float64}=[180.0, 395.0, 590.0], 
                                   model::Symbol=:smagorinsky)
    println("📈 LES Reynolds Number Scaling Study")
    println("===================================")
    println("Re_τ range: $(Re_tau_range)")
    println("SGS model: $(model)")
    println()
    
    results = []
    
    for (i, Re_tau) in enumerate(Re_tau_range)
        println("Case $(i)/$(length(Re_tau_range)): Re_τ = $(Re_tau)")
        println("-" * "="^40)
        
        # Adjust resolution based on Reynolds number
        resolution = max(32, Int(round(Re_tau / 10)))
        
        result = run_les_turbulence_demo(Re_tau=Re_tau, turbulence_model=model, 
                                        resolution=resolution, verbose=false)
        push!(results, result)
        
        # Print scaling metrics
        turb_stats = result.turbulence_statistics
        max_vel = get(turb_stats, "max_velocity_magnitude", NaN)
        tke = get(turb_stats, "turbulent_kinetic_energy_estimate", NaN)
        mean_nu_sgs = get(turb_stats, "mean_subgrid_viscosity", NaN)
        
        println("  Max velocity: $(max_vel) m/s")
        println("  TKE estimate: $(tke) m²/s²")
        println("  Mean νₛₘ: $(mean_nu_sgs) m²/s")
        println("  Converged: $(result.converged)")
        println()
    end
    
    # Scaling analysis
    println("REYNOLDS SCALING ANALYSIS")
    println("="^50)
    println("Re_τ\\t\\tMax Vel\\t\\tTKE\\t\\tMean νₛₘ")
    println("-"^50)
    
    for (Re_tau, result) in zip(Re_tau_range, results)
        stats = result.turbulence_statistics
        max_vel = get(stats, "max_velocity_magnitude", NaN)
        tke = get(stats, "turbulent_kinetic_energy_estimate", NaN)
        mean_nu_sgs = get(stats, "mean_subgrid_viscosity", NaN)
        
        @printf "%.0f\\t\\t%.3f\\t\\t%.2e\\t%.2e\\n" Re_tau max_vel tke mean_nu_sgs
    end
    
    return results
end

# Main execution
if abspath(PROGRAM_FILE) == @__FILE__
    println("LES Turbulence Demo Examples")
    println("===========================")
    println()
    
    println("1. Basic LES simulation with Smagorinsky model")
    basic_result = run_les_turbulence_demo(Re_tau=395, turbulence_model=:smagorinsky, verbose=true)
    
    println("\\n\\n2. Subgrid-scale model comparison")
    comparison_results = run_sgs_model_comparison()
    
    println("\\n\\n3. Reynolds number scaling study")
    scaling_results = run_reynolds_scaling_study()
    
    println("\\n🎉 All LES turbulence demos completed successfully!")
end